Doublet Ground Research Articles

The properties of thulium vanadate — An example of molecular field behaviour

The ground state of thulium vanadate is a non-Kramers doublet which is split by a Jahn-Teller distortion at TD=2.1 K. Below TD the behaviour accords with predictions of molecular field theory. Magnetic moment, magnetic susceptibility and specific heat measurements show that above TD the ground doublet has g-values gc=10.1S, ga=ga′=0 and that the splitting of the doublet at absolute zero is 3.0 cm−1. Der Grundzustand des Thulium Vanadats ist ein Nicht-Kramers Dublett, dessen Entartung bei TD=2.1 K durch eine Jahn-Teller-Aufspaltung aufgehoben wird. Das Verhalten unterhalb TD kann sehr gut mit der Molekularfeld-Theorie beschreiben werden. Messungen des magnetischen Moments, der magnetischen Suszeptibilität und der spezifischen Wärme zeigen dass der Grundustand oberhalb TD die g-Faktoren gc=10.1 und ga=ga′=0 hat. Die Aufspaltung beim absoluten Nullpunkt wurde zu 3.0 cm−1 bestimmt.

Paramagnetic resonance and relaxation of Dy3+ and Er3+ in YAsO4 and YVO4

AbstractParamagnetic resonance experiments on Dy3+ ions in (Y, Dy)VO4 (100:1) showed both the transition in the ground doublet and the transition in the first excited doublet. The energy gap between both doublets was estimated by comparing the line intensities at various temperatures. By means of a pulse saturation technique at X‐band frequencies paramagnetic relaxation times have been observed in the temperature range of liquid helium as a function of the angle between the optical axis and the magnetic field, and additionally in the case of (Y, Dy)VO4, as a function of crystal size and concentration 100:1, 20:1, and 5:1).

Molecular Orbital Study of NH2, NO2, and NF2

The orthogonality constrained basis set expansion method has been used to determine SCF wavefunctions for ground and lower excited doublet states of NH2, NO2, and NF2. The calculations on NO2 and NF2 were performed using a minimal basis set, while both minimal and extended bases were used in the study of NH2. Geometries and dipole moments of the various states were obtained and found to be in good agreement with available experimental data. Calculated vertical and 0–0 transition energies in these systems were also found to approximate the experimentally determined excitation energies.

Ferromagnetic resonance in cobalt doped magnesium and manganese ferrites

Measurements of the change in anisotropy field and ferromagnetic resonance linewidth due to doping magnesium ferrite and manganese ferrite with cobalt are reported. A large effect upon anisotropy and relatively small effect on the linewidth is observed. The behaviour is explained in a broadly satisfactory manner in terms of a ion theory of the anisotropy and the longitudinal relaxation model, assuming a simple form for the ground doublet energy levels of the Co2+ ion on octahedral sites. Only about one third of the cobalt ions substituted into the magnesium host contribute to the anisotropy energy, whereas all the ions do so in the other host. The relatively weak effect upon the linewidth is interpreted to show that the Co2+ ion populations relax between the doublet states in approximately=10-13s.

EPR Observations of Temperature Dependent Level Crossing for Gd3+ in LaCl3

Observations by electron paramagnetic resonance of LaCl3 single crystals containing very small concentrations of Gd3+ have revealed previously unresolved structure in the Gd3+ spectrum at temperatures between 150 and 294°K. A multiple crossing of the S7/28 ground doublets occurs in this temperature range, and the ability to make correct M8 assignments to the EPR transitions results in values for the spin-Hamiltonian parameters which differ from those reported previously.

The temperature change in the electron-spin resonance of Cu 2+ in CaO

The marked differences between the low and high temperature values of g and A in the ESR of CaO:Cu 2+ are explained by assuming a moderate Jahn-Teller effect and the coalescence and motional narrowing of the vibronic ground doublet and excited singlet lines and by including off-diagonal S and I> operators.

Endor of 173 Yb 3+ on tetragonal sites in calcium fluoride: determination of the crystal field parameters

Endor experiments have been performed on 173 Yb at tetragonal sites in CaF 2 . The spin-Hamiltonian describing the frequencies of the endor lines contains many small terms, which arise in second order from matrix elements of Zeeman and hyperfine interactions that couple the ground doublet to excited states of the J = 7/2 manifold. From the experimental values of these small terms the energies of the excited states of this manifold are deduced. This information is used together with g values of the lowest doublet for both J = 7/2 and J = 5/2 manifolds, and the energy of the lowest doublet of the J = 5/2 manifold, to calculate the following crystal field parameters (all in cm -1 ): B 2 0 = + 8.4 ( 1.3 ) ; B 4 0 = + 0.19 ( 0.03 ) ; B 6 0 = + 0.054 ( 0.005 ) ; B 4 4 = + 2.8 ( 0.4 ) ; B 6 4 = − 0.735 ( 0.07 ) . . The measured value of the nuclear electric quadrupole interaction for 137 Yb( I = 5/2) is sepa­rated into a component due to the field gradient from the 4f electrons and one due to the field gradient from the surrounding lattice. Comparison of the latter component with the value of B 2 0 gives (1–γ∞)/(1–σ 2 ) = 75±18, considerably smaller than values of this ratio predicted theoretically or found in earlier experimental investigations. The most likely cause of this low value is the considerable contribution of covalent effects to B 2 0 .

Paramagnetic Resonance ofHo3+in a Trigonal Site in SrF2

A paramagnetic-resonance spectrum of ${\mathrm{Ho}}^{3+}$ in a trigonal site in Sr${\mathrm{F}}_{2}$ was observed. The spectrum is characteristic of a non-Kramers ion, and the asymmetric line shape indicates that the non-Kramers ground doublet requires low-symmetry strain distortions to split the doublet and observe paramagnetic-resonance transitions of the magnetic dipole type. The spectrum is interpreted in terms of a standard spin Hamiltonian for a non-Kramers doublet with the parameters ${g}_{\ensuremath{\parallel}}=18.2\ifmmode\pm\else\textpm\fi{}0.1$, ${\ensuremath{\Delta}}_{0}=0.033\ifmmode\pm\else\textpm\fi{}0.001$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $|A|=0.397\ifmmode\pm\else\textpm\fi{}0.005$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The possibility of observing paraelectric resonance in this site, which lacks inversion symmetry, was investigated. A discussion of various possible eigenfunctions, transitions, and line shapes in crystal fields of threefold and fourfold symmetry is given.

Detection ofAl2O3:Fe2+by Acoustic Paramagnetic Resonance

We have observed acoustically a spin-resonance line that we believe is due to the ground state of ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$: ${\mathrm{Fe}}^{2+}$. This spin system has not previously been detected by resonance techniques. The transition has a ${g}_{\mathrm{II}}$ of 3.40\ifmmode\pm\else\textpm\fi{}0.04, and its variation with magnetic field direction suggests that a singlet level is also present, at an energy, when the field is parallel to the $c$ axis, of not less than 6 ${\mathrm{cm}}^{\ensuremath{-}1}$ above the ground doublet. From the intensity of the line, it was estimated that the magneto-elastic coefficient ${[\frac{1}{4}{({G}_{11}\ensuremath{-}{G}_{12})}^{2}+{{G}_{16}}^{2}]}^{\frac{1}{2}}$ has a value of not less than 15 ${\mathrm{cm}}^{\ensuremath{-}1}$ ${(\mathrm{unit}\mathrm{strain})}^{\ensuremath{-}1}$. These results are consistent with recent calculations by Stevens and Walsh.

Symmetric charge transfer involving 2P3/2 and 2P1/2 Kr+ and Xe+ ions

A technique which employs a carefully controlled electron-impact ion source is used to show that the two ground doublet states of both Kr+ and Xe+ undergo symmetric charge transfer with near equal efficiency in the energy range 300-2500 eV.

Temperature and Magnetic Field Dependence of the Spin-Lattice Relaxation Rates forEr3+,Pr3+, andTb3+in Anhydrous LaCl3

Using the plused-saturation technique at 15.4 GHz, we measured the spin-lattice relaxation rates of La${\mathrm{Cl}}_{3}$:Er, La${\mathrm{Cl}}_{3}$:Pr, and La${\mathrm{Cl}}_{3}$:Tb over the temperature range 0.24-4.2\ifmmode^\circ\else\textdegree\fi{}K and analyzed the results within the framework of the Van Vleck---Orbach theory. In addition, from measurements at about 9 GHz made by us and by others on some of the same samples, we obtained information on the magnetic field (or frequency) dependence of the various terms in the relaxation-rate expression. For the erbium and terbium systems, the temperature dependence was consistent with the simple theory. However, for the praseodymium system, a "phonon bottleneck" apparently occurred at low temperatures. The variation of the relaxation rate with the microwave frequency was in agreement with theory for the Kramers ion ${\mathrm{Er}}^{3+}$, and consistent with theory for the bottlenecked non-Kramers ion ${\mathrm{Pr}}^{3+}$. The non-Kramers ion ${\mathrm{Tb}}^{3+}$ has a somewhat unusual frequency dependence, theoretically, due to the splitting of its ground doublet by the La${\mathrm{Cl}}_{3}$ crystal field. The experimental frequency dependence for this ion was in substantial agreement with theory for the Raman and Orbach rates, but not quite as strong as predicted for the direct rate.

Endor of 171 Yb 3+ and 173 Yb 3+ on cubic sites in calcium fluoride

The energy level scheme for 4 f 13 in a cubic crystal field is relatively simple. The effect of a perturbation Hamiltonian containing electron and nuclear Zeeman terms and magnetic dipole and electric quadrupole hyperfine interactions can therefore be calculated easily, especially as the experimental results only justify calculation to second order. The second-order effects give several small unusual terms in the spin-Hamiltonian for the ground doublet Γ 7 . The high precision of endor experiments on 171 Yb and 173 Yb make it possible to measure these small terms and confirm that their magnitude is consistent with the second-order calculation. From the size of the second-order terms we also obtain a value for the energy of the Γ 8 state of the lowest J = 7/2 manifold (604 ± 10 cm -1 ), and a value for the electric quadrupole interaction in the free ion. We have also attempted to measure a hyperfine structure anomaly in order to estimate the contribution of core polarization to the hyperfine interaction, but such an anomaly is too small to be detectable with the precision of measurement we were able to achieve.

T1andT2for Orbach Relaxation Processes

The master equation for the density matrix of the ionic levels involved in the relaxation process described by Orbach is developed in a form valid for low temperatures. In the absence of degeneracies, the equations for the diagonal elements of the density matrix are the rate equations for the populations which have been solved before; and the equations for the off-diagonal elements show that ($\frac{1}{{T}_{2}}$), the linewidth for a transition between two levels, is given by one-half the sum of the phonon-induced rates out of those levels. Cases in which the inverse lifetimes of the excited states are not small compared with the splitting of the doublets are investigated, and we find that the modification of ${T}_{1}$ can be quite significant, but that the effect on ${T}_{2}$ is slight in all cases. For ${\mathrm{Ce}}^{3+}$, ${\mathrm{Nd}}^{3+}$, and ${\mathrm{Sm}}^{3+}$ in the double nitrates, we find that ${T}_{1}={T}_{2}$ within 12.5% for the magnetic field perpendicular to the symmetry axis for all conditions. For ${\mathrm{Ce}}^{3+}$ in LaMg double nitrate with the field perpendicular to the symmetry axis, measurements at 10 Gc/sec should give ${T}_{1}={T}_{2}$ within 3%, whereas the experimental result reported by Stapleton and Brower is ${T}_{1}=13{T}_{2}$. It is found that spin-spin interactions between the ground doublet and the excited doublet cannot be the cause of the discrepancy, but that a near-universal bottlenecking of a part of the phonon modes would lead to an explanation of the linewidth measurements and not be at variance with the size and concentration dependence of ${T}_{1}$ thus far reported for the double-nitrate crystals. This hypothesis is based on the calculations of Orbach and Vrederoe, which show that the lifetime of the transverse phonon modes may be much longer than that for the longitudinal modes. Further, the transverse phonons should produce the greater part of the orbitlattice interaction. This hypothesis suggests that a true spin-lattice ${T}_{1}$ would be measured only at very low concentrations, and that with increasing concentrations a bottleneck would develop so that the apparent relaxation time would increase with concentration until the bottlenecked relaxation became comparable with the rate due to other unbottlenecked phonons acting in parallel with the bottle-necked phonons. The experiments of Adde and Geschwind appear to show some aspects of this behavior.

Phase Memory in Electron Spin Echoes, Lattice Relaxation Effects in CaWO4: Er, Ce, Mn

The electron-spin-echo phase memory ${T}_{M}$ has been studied both experimentally and theoretically for the specific case in which it is limited by the lattice relaxation processes occurring in the sample. The relevant mechanism is as follows. Lattice relaxation of any spins, whether or not they belong to the species being observed, causes fluctuations in the local fields and so destroys the relations between precessional phases which lead to the generation of echoes. The effect of these fluctuations on the echo amplitude can be calculated by taking an ensemble average for the precessing spins and for all the environmental spins which give rise to significant time variations of the local fields in the sample. The problem reduces to that of finding a time and a space average. The space average has been obtained here by assuming a random distribution of spins in the paramagnetic sample, and by applying the statistical methods of Margenau. In order to obtain the time average, two models have been chosen to represent the time variation of the components ${\ensuremath{\mu}}_{z}$ for the relaxing spins. In one model, the ${\ensuremath{\mu}}_{z}$ are treated as Gaussian random variables (Gauss-Markoff model), and in the other the spins are assumed to make sudden jumps at random times between the "spin-up" and "spin-down" quantum states (sudden-jump model). Different forms of echo envelope are derived for the two models. Further differences in behavior will be observed, according to whether the sample is singly or doubly doped. If the sample contains only one spin species, ${T}_{M}$ becames shorter as the temperature is raised and as the lattice relaxation time ${T}_{1}$ is reduced. Initially, ${T}_{M}$ is limited by local field fluctuations and may be considerably shorter than ${T}_{1}$. Eventually, as the lattice relaxation of the precessing spins themselves becomes the dominant factor, ${T}_{1}$ and ${T}_{M}$ tend to the same value. If the sample contains two species $A$ and $B$, where $B$ relaxes more rapidly than $A$, then ${T}_{M}(A)$ and ${T}_{M}(B)$ both begin by shortening as ${T}_{1}(B)$ is reduced. For very small values of ${T}_{1}(B)$, however, ${T}_{M}(A)$ lengthens again. The rapidly fluctuating local fields due to the $B$-spins produce a diminishing effect on the $A$ spins, the phenomenon being analogous to motional narrowing. The form of the $A$-spin echo envelope in the limit of rapid $B$-spin relaxation does not depend on the model chosen to represent the time variation of ${\ensuremath{\mu}}_{z}$ during the relaxation of the $B$ spins.Experimental results are presented for two-pulse and three-pulse echoes, and are compared with the calculations. The material is CaW${\mathrm{O}}_{4}$ doped with Ce and Er or with Mn and Er. At the lower temperatures, the results are in moderately good agreement with the Gauss-Markoff theory. At higher temperatures, the results can only be explained by assuming that the transition rate between the levels of the Er ground doublet is an order of magnitude higher than the transition rate inferred from ${T}_{1}$ measurements. It is tentatively suggested that this may arise from the fact that ${T}_{M}$ depends on the arithmetic sum of the upward and downward transitions, whereas ${T}_{1}$ merely measures the algebraic sum, i.e., the excess of down-ward over upward transitions. If some form of spin-spin interaction is taking place, or if there is a phonon bottleneck (or any other mechanism causing transfers of energy within the spin system), the absolute and the net transition rates will cease to bear the usual thermodynamic relation to one another. In the present case it is suggested that energy transfer in the Er spin system is accelerated by the exchange of real phonons as soon as there is a significant population of the first excited doublet. The possible effects of spin clustering and of nonmagnetic dipolar interactions on the form of the echo decay envelopes are also briefly discussed.

Spin-lattice relaxation time measurements of Tb3+ in CaWO4

The spin-lattice relaxation time T1 of Tb3+ in CaWO4 has been measured in the temperature range 13-9 °K. The dependence of the relaxation rate on temperature can be described by This suggests that the first excited state lies at 788 °K above the ground doublet, which is confirmed by an absorption experiment. These results are compared with those predicted by a set of crystal field parameters suggested by Shekun.

The hyperfine structure of 161Dy in dysprosium salts

The Mössbauer technique was used to investigate the low temperature (4.2°K) hyperfine structure of 161Dy in the following paramagnetic salts: Group 1; Dy-oxalate, Dy-acetate, DyF 3·5 H 2 O, Dy( NO 3) 3·6 H 2 O, DyPO 4·5 H 2 O, Dy( MoO 4) 3, DyFeO 3, DyMn 2 O 5, DyAlG; and Group 2; Dy 2 O 3, DyCl 3·6 H 2 O, Dy-ethyl sulfate. In all cases the observed spectra were consistent with a collinear hyperfine magnetic field and axially symmetric EFG. This requires a ground doublet with the property g ⊥ = 0 ≠ g ‖. In Group 1 compounds the observed hfs interactions were within 4 per cent of the free ion hyperfine interaction, g O β N H eff = 820 ± 20 Mc/ s for a doublet ‖ ± J z 〉 with J s = 15 2 . The three compounds in Group 2 had g O β N H eff = 727, 675 and 446 Mc/ s respectively. The results in Group 1 imply a ground doublet with g ‖ ≅ 19·6 and in Group 2 we have values for g ‖ of 17·2, 16·0 and 10·6 for the three compounds, respectively.

High Field Zeeman Effect of Pr3+ Absorption Lines in CaF2

The Zeeman effect of the absorption lines of Pr 3+ in CaF 2 was investigated photographically using pulsed magnetic field up to 130kOe at 77°K and 4.2°K. Some strong absorption lines were determined to be associated with the transitions from the ground doublet to the singlets in the crystal field of C 3 v symmetry and the transitions were found to be of electric dipole origin.

EPR SPECTRA OF PAIRS OF INTERACTING RARE-EARTH IONS

The EPR spectra of interacting pairs of Dy3+, Tb3+, and Ho3+ ions in rare-earth ethyl sulfates have been studied in order to determine the nature and magnitude of the interactions. The departures from dipole–dipole interaction are mostly rather small, except for the interaction between a pair of Dy3+ ions, one of which is in the ground doublet and the other in the first excited doublet at 16 cm−1. A discussion is given of the difficulties of differentiating between the effects of electric quadrupole–quadrupole interaction and virtual phonon exchange interaction.

Electron Spin Resonance of Dy3+ in LaCl3

We have examined the electron spin resonance spectrum of trivalent dysprosium in a single crystal of anhydrous lanthanum trichloride and have identified weak forbidden resonances as originating from the ground doublet in sites of distorted and essentially undistorted crystal symmetry. Also present in the spectrum is an allowed transition between the energy levels of the first excited doublet. The ESR spectrum due to the ground doublet in an undistorted site can be described by an axially symmetric spin Hamiltonian with S=½, g∥=10.43±0.05 and g⊥<1. The ESR line from the excited-state transition fits an axially symmetric spin Hamiltonian with S=32 involving the operators HiSi, Si2, and HiSi3; the latter terms being necessary to account for the effects of another doublet 0.135±0.01 cm−1 away. This measurement of the zero-field splitting is in good agreement with the optical value of 0.15 cm−1. The remaining parameters of the S=32 spin Hamiltonian are also in reasonable agreement with values computed from crystal-field theory.

Spin—Lattice Relaxation of Rh(II) in Single Crystals of ZnWO4

The spin-lattice relaxation time T1 of Rh(II) in a single crystal of ZnWO4 has been measured in the temperature range 1.5°—110°K. In the region 56°—110°K relaxation occurs by an Orbach process. From the temperature dependence of this process, the separation of the first excited Kramers doublet E′ from the ground doublet E″ is found to be 320 cm−1, and the lifetime of the excited state 1.7×10−11 sec. At low temperatures, the relaxation times are relatively short and depend upon the direction of the applied magnetic field H. With H aligned along the a, b, or c crystalline axes an anomalously strong dependence of T1 on temperature is observed.